(2004) 224: 37–47 _
C Springer 2005
LONG-TERM SOLAR ACTIVITY: DIRECT AND INDIRECT STUDY
I. G. USOSKIN1 and G. A. KOVALTSOV2
Geophysical Observatory (
(Received 1 September 2004; accepted 23 September 2004)
Abstract. The series of directly observed sunspot numbers is nearly 400 years long. We stress that
the recently compiled group sunspot number series is an upgrade of the old Wolf series and should
always be used before 1850. The behavior of solar activity on longer time scales can be studied
only using indirect proxies. Such proxies as aurorae occurrence or naked-eye sunspot observations
are qualitative indicators of solar activity but can be hardly quantitatively interpreted. Cosmogenic
isotope records provide a basis for quantitative estimate of the past solar activity. Here we overview
the main methods of the long-term solar activity reconstruction on the centennial to multimillennia
time scale. We discuss that regression-based reconstructions of solar activity lead to very uncertain
results, while recently developed physics-based models raise solar activity reconstruction to a new
level and allow studying its behavior on a multimillennia time scale. In particular, the reconstructions
show that the recent episode of high solar activity is quite unusual in the multimillennia time scale.
The sunspot number (SN) series is the longest record of directly observed solar
activity, which started in 1610 and covers about 400 years. During this period
SN was varying between the nearly spotless Maunder Minimum and the recent
unusually high activity when SN reached the average value of about 75. The main
features of solar activity on the decennial–centennial time scale were summarized,
e.g., by Vitinsky (1986) or Usoskin and Mursula (2003). However, it is important to
know the behavior of solar activity on even longer time scales for many reasons, in
particular for the solar/stellar dynamo theory and for research on long-term solarterrestrial
relations (“space climate”). Since there were no regular observations in
the pre-telescopic era, indirect methods are used for the purpose. Here we overview
the main methods and results of the long-term solar activity reconstruction on the
centennial to multimillenial time scale.
2. Sunspot Number Series
Until recently the longest series of sunspot observations was the famous Wolf
sunspot number (called WSN henceforth) which was primarily compiled by Rudolf
Figure 1. The annual series of sunspot numbers: Group sunspot numbers (GSN, solid line) andWolf
sunspot numbers (WSN, dotted line).
Figure 2. The amplitude of solar cycles according to GSN (thick lines and black squares), original
WSN published in 1861 (dotted line with open diamonds) and the corrected “modern” WSN (thin
line with grey dots).
Wolf of Z¨urich Observatory and then continued using the same method (Waldmeier,
1961) (since the 1980s WSN is provided by the Royal Observatory of Belgium).
The official WSN starts in 1749, and before that only yearly WSN values are
available (Figure 1). The WSN series uses only one (primary) observer for each
day with all gaps being interpolated without notes (for details see, e.g., Hoyt and
Schatten, 1998). Therefore, the WSN series is a combination of direct observations
and interpolations for the period before 1849 with all the raw information hidden,
which makes it impossible to estimate its uncertainties (see, e.g., Vitinsky et al.,
1986; Hoyt et al., 1994; Wilson, 1998; Letfus, 1999). WSN contains not only
sunspot but also geomagnetic data as illustrated by Figure 2. After publishing his
original sunspot series in 1861 (Wolf, 1861),Wolf corrected it using the “magnetic
needle” (geomagnetic inclination range) data measured in Milano (see the full story
in Hoyt and Schatten, 1998). Note that the original WSN series is much closer to
the Group spot numbers (GSN) than the corrected WSN which is widely used now.
Thus, the WSN series can be analyzed only for the period since 1849 or, with
caveats, since 1749.
Recently a new updated sunspot series, called the Group sunspot number (GSN)
series (see Figure 1), was presented by Hoyt and Schatten (1998), which contains
80% more raw information and is more homogeneous than WSN (Hoyt and
LONG-TERM SOLAR ACTIVITY: DIRECT AND INDIRECT STUDY 39
Schatten, 1998; Letfus, 1999; Hathaway et al., 2002). Although GSN still contain
some uncertainties, it is important that all raw information is available which
allows for independent re-analysis, error estimate, and statistical studies (Usoskin
and Mursula, 2003). The GSN series is strongly recommended for analysis of
sunspot activity before 1850. It should be noted that WSN and GSN are not different
alternative proxies of solar activity but rather GSN is an upgrade of the WSN
series. We note that even GSN series is not finalized, and new archival results on
sunspot observations appear, filling some gaps in GSN (Vaquero, 2004).
3. Indirect Proxy
The only way to study solar activity in the pre-telescopic era is related to the so
called indirect solar proxies.
Such a proxy is the record of visual observations of aurorae borealis in middlelatitudes
which are caused by enhanced geomagnetic activity due to transient interplanetary
phenomena (e.g., Schove, 1983; Silverman, 1983, 1992, 1998; K˘rivsk´y
and Pejml, 1988). Fragmentary records of aurorae can be found in Occidental and
Oriental sources since antiquity. These data are sensitive to long-term changes of
the geomagnetic field. Also, because of the phenomenon’s short duration and low
brightness, the probability of seeing aurora can be affected by a number of factors
(clouds, the phase of the Moon, season, etc.). The fact that these observations were
not systematic in early times makes it difficult to produce a homogeneous data set.
Some fragmentary data on naked-eye observations of sunspots exist for quite
early times, mostly from Oriental sources (see,
Wittmann and Xu, 1987; Yua and Stephenson, 1988). Spots on the Sun are mentioned
in official Chinese and Korean chronicles from 165 BC to 1918 AD. While
these chronicles are fairly reliable, these data are not straightforward to interpret
since they can be influenced by meteorological or other phenomena (e.g., dust loading
in the atmosphere due to dust storms or volcano eruptions facilitates sunspot
observations). Moreover, records of sunspot observations in the official chronicles
depended on the dominant traditions during specific historical periods. Direct comparison
of the Oriental naked-eye sunspot observations and European telescopic
data shows that the naked-eye observations can serve only as a qualitative indicator
of the sunspot activity but can be hardly quantitatively interpreted (see, e.g.,Willis,
1996 and references therein).
The most useful proxy of solar activity is formed by the data on cosmogenic
radionuclides, e.g., 10Be and 14C, which are produced by cosmic rays in the Earth’s
atmosphere (e.g, Stuiver and Quay, 1980; Beer et al., 1990; Bard, 1997; Beer, 2000).
Cosmic rays are the major source of cosmogenic nuclides in the atmosphere (excluding
anthropogenic factors during last decades) with the maximum production being
in the upper troposphere/stratosphere. After a complicated transport in terrestrial
reservoirs (atmosphere, ocean, biosphere) they are stored in natural archives such
as polar ice, trees, marine sediments, etc. Because of the heliospheric modulation
of the cosmic ray intensity at the Earth’s orbit, the cosmogenic isotope production
depends inversely on solar activity. An important advantage of the cosmogenic
data is that primary archiving is done routinely in a similar manner throughout
the ages, and these archives are measured nowadays in laboratories using modern
techniques. If necessary, all measurements can be repeated and improved as has
been done for some radiocarbon samples. In contrast to fixed historical archival
data (such as sunspot or auroral observations) this approach, together with absolute
independent dating of samples, allows for homogeneous data sets with stable
quality. Cosmogenic isotope data are the only regular indicator of solar activity on
the very long-term scale but they cannot always resolve details of individual solar
cycles. Redistribution of the nuclides in the terrestrial reservoirs and archiving may
be affected by local and global climate/circulation processes which are to a large
extent unknown in the past. However, a combined study of different nuclides data,
whose responses to terrestrial effects are very different, may allowfor disentangling
external and terrestrial signals.
4. Solar Activity Reconstruction from Proxy Data
4.1. MATHEMATICAL METHODS
There are numerous attempts to extend the sunspot series back in time using
extrapolations of its statistical properties (e.g., De Meyer, 1998; Rigozo et al.,
2001). Actually, it is not a reconstruction based upon measured or observed quantities
but rather a “post-diction.” Although often used for predictions, such a method
can hardly be applied for a reliable reconstruction of solar activity. In particular, it
assumes that the time series is stationary, i.e. that all information on its future/past
is contained in a limited time sample. Clearly such models cannot include periods
exceeding the time span of observations upon which the extrapolation is based.
Regressions are the most used method of solar activity reconstruction from
proxy data (see, e.g., Stuiver and Quay, 1980; Ogurtsov, 2004).Aphenomenological
regression (either linear or nonlinear) is built between proxy data set and the directly
measured solar activity for the available “training” period (since 1750 for WSN or
since 1610 for GSN). Then this regression is extended backwards to evaluate SN
from the proxy data. The main shortcoming of the regression is that this method
depends on the time resolution and “training” period. The former is illustrated by
Figure 3 which shows the scatter plot of the 10Be concentration vs. GSN for the
annual and 11-year smoothed data. One can see that the slope of the 10Be-vs.-GSN
relation within individual cycles is significantly different (about−500 g/at) from the
slope of long-term relation (about−100 g/at), i.e., individual cycles do not lie along
the line of 11-year averaged cycles. Therefore, the formal regression built using
the annual data for 1610–1985 yields a much stronger GSN-vs.-10Be dependence
LONG-TERM SOLAR ACTIVITY: DIRECT AND INDIRECT STUDY
Figure 3. Scatter plot of smoothed group sunspot numbers vs. (2-year delayed) 10Be concentration.
(a) Annual (connected small dots) and 11-year averaged (big open dots) values. (b) Best-fit linear
regressions between the annual (dashed line) and 11-year averaged values (solid line). The dots are
the same as in panel (a).
than for the cycle-averaged data (see Figure 3b). Accordingly, when applying an
annual-based regression to the long-term smoothed 10Be (and other proxy) data
may result in erroneous evaluation of the sunspot number. Also, the use of WSN
instead of GSN before 1850 to build a regression can lead to additional errors in the
reconstruction, since WSN overestimates the SN level for the eighteenth century
(Section 2). We note that earlier regression works (before 1998 when Hoyt and
Schatten published their final GSN series) were based on WSN series and should
Sometimes a fit of a mathematical model to indirect proxy data is used, which
is a combination of the extrapolation and proxy methods. In such models a mathematical
extrapolation is fitted to some proxy data for the time when direct data
are not available, e.g., Schove (1955) fitted the slightly variable but phase-locked
carrier frequency (about 11 years), to fragmentary data from naked-eye sunspot
observations or auroral sightings. This approach has been recently modified using
nonlinear relations (Nagovitsyn, 1997), but its shortcomings still limit the reliability
of the reconstruction. We note that these works yield too high sunspot activity
during the Maunder minimum.
4.2. PHYSICS-BASED MODELS
Anew step in long-term solar activity reconstruction has been made recently, which
is a development of the proxy method where physics-based models are used, instead
of a phenomenological regression, to link SN with the cosmogenic isotope
production (Beer et al., 2003; Usoskin, 2003; Solanki, 2004). Due to recent theoretical
developments, it is now possible to construct the chain of physical models
to simulate the entire link between solar activity and cosmogenic data. The first
model (Solanki, 2000, 2002) relates the open solar magnetic flux to SN (through
the magnetic flux in sunspots). Although this model is based on physical principles,
it contains one adjustable parameter, the decay time of the open flux, which cannot
be measured or theoretically calculated and has to be found fitting the model to
data. Open flux data since 1975 were used to fix this parameter (Solanki et al.,
2000, 2002). The open magnetic flux is directly related to the global interplanetary
magnetic field which modulates the spectrum of cosmic rays at the Earth’s
orbit. The next model (Usoskin et al., 2002a) calculates the cosmic ray spectrum
X(P,_), where _ is the heliospheric modulation strength and P is particle’s rigidity,
from the open magnetic flux. For studies of long-term changes of the cosmic
ray flux, the parameter _ alone adequately describes the modulation of the cosmic
ray (Caballero-Lopez and Moraal, 2004). The connection between the cosmogenic
isotope production rate, Q, at a given location and the cosmic ray flux is given by
Q(θ) = _ ∞
X(P,_) · Y (P)dP, (1)
where θ is the geomagnetic latitude, Pc is the local cosmic ray rigidity cutoff,
and Y (P) is the differential yield function of cosmogenic isotope production (see
Castagnoli and Lal (1980) for 14C, and Masarik and Beer (1999) or Webber and
Higbie (2003) for 10Be). The abundance of 10Be in polar ice is assumed to be
directly proportional to its atmospheric production rate (Beer et al., 1990, 2003;
Masarik and Beer, 1999; Usoskin et al., 2002a) owing to its short residence time
in the atmosphere and relatively simple precipitation process. On the other hand,
a complicated global carbon cycle is involved between the production of 14C in
the atmosphere and its final deposition in tree rings (see, e.g., Damon et al., 1978;
Stuiver and Quay, 1980). Because of the global nature of the carbon cycle and its
long attenuation time, the radiocarbon is globally mixed before the final deposition,
and Equation (1) should be integrated over the globe. Thus, a physics-based model
exists for every step linking the solar activity to cosmogenic isotope content. The
validity of this link was verified by Usoskin et al. (2002b) who calculated the
expected concentration of 10Be in polar ice from the GSN record and showed that
it corresponds well to the measured concentration.
Inverting the physics-based model one can quantitatively evaluate the solar activity
from the measured cosmogenic isotope abundance. Due to strong nonlinearity
of the model, its inversion cannot resolve individual 11-year cycles, and only cycleaveraged
slow changes of the solar activity can be reconstructed (Usoskin et al.,
2003, 2004). Using the data on 10Be
Usoskin (2003) reconstructed 11-year averaged SN since 850 AD (Figure 4). This
result reproduces the four known grand minima of solar activity – Maunder (1645–
1715), Sp¨orer (around 1500 AD), Wolf (around 1300 AD), and tiny Oort (around
1050 AD) minima (cf., e.g., Peristykh and Damon, 2003). Later Solanki et al. (2004)
reconstructed 10-year averaged sunspot numbers from the 14C content in tree-rings
throughout the Holocene and estimated its uncertainties (see Figure 4). The slightly
negative values during the grand minima are an artifact, they are compatible with
LONG-TERM SOLAR ACTIVITY: DIRECT AND INDIRECT STUDY 43
Figure 4. 10-year averaged sunspot numbers: Actual group sunspot numbers (thick grey line) and the
reconstructions based on 10Be (thin curve, Usoskin, 2003b) and on 14C (thick curve with error bars,
Solanki, 2004). The horizontal dotted line depicts the high activity threshold, 50.
the absence of sunspots within the error bars. One can see that the two SN reconstructions
are consistent with each other, but with the 10Be-based one being
systematically higher, especially in the early part of the millennium. This is expected
since Usoskin (2003) evaluated the upper limit of SN assuming the purely
local production of 10Be deposited in polar ice. Similar physics-based approach
was used by Beer et al. (2003) who also reconstructed the solar activity on the multimillennia
time scale using the 10Be
data from GISP2 core in
not reconstruct SN but presented the reconstructed modulation strength _ skipping
the last step in the physics-based model inversion, which may introduce additional
uncertainties. The two reconstructions, based on 10Be (Beer et al., 2003 – these
results are still preliminary) and on 14C (Solanki et al., 2004) data, are similar to
each other (J¨urg Beer, personal communication). Taking into account that the two
models are independent and use different isotopes with different geochemical fate,
this verifies the reliability of the long-term solar activity reconstruction.
4.3. VERIFICATION OF RECONSTRUCTION MODELS
As a verification of a SN reconstruction, its comparison with the actual GSN data
for the last centuries is usually used. However, regression-based models cannot be
tested in thisway since thiswould require long set of independent direct data outside
the “training” interval. It is usual to include all available data into the “training”
period to increase the statistics of a regression, which rules out a possibility to test
the model data. On the other hand, such a comparison to the actual GSN since 1610
can be regarded as a direct test for a physics-based model since it does not include
phenomenological relation over the same interval (the only adjustable parameter in
the model by Solanki et al. (2000) was fixed using data for 1975–2002). The period
of the last four centuries is pretty good for the testing purpose since it includes
the whole range of solar activity from nearly spotless Maunder minimum to the
modern period of very active Sun. The agreement between the measured GSN
and the 14C-based reconstruction is excellent (the correlation coefficient r = 0.93
with the RMS deviation between the two series being 6) for the period 1610–1900
(Solanki et al., 2004). The agreement between GSN and 10Be-based reconstruction
(Usoskin, 2003b) is also good (r = 0.78,RMS=10 for 1700 –1985). This validates
the reliability of the physics-based reconstruction.
Note that both mathematical and physics-based models use an assumption on
the constancy of involved processes over the studied time scale. However, they
may change significantly through the ages. On the centuries-millennia time scale,
the most important changes are long-term changes of the geomagnetic field, when
both the geomagnetic dipole momentum changes and the dipole axis migrates (see,
e.g., Hongre, 1998). These changes modify the global shielding from cosmic rays,
changing thus the relation between SN and cosmogenic proxies. This may also
distort interpretation of the frequency of aurorae watching in the past. While geomagnetic
changes may distort the phenomenological reconstruction of sunspot
activity from proxy data, the physics-based model can naturally account for the geomagnetic
changes. Generally speaking, changes in the climate at the observational
site may also affect the solar activity reconstruction. However, the global climate
is known to be pretty stable during the Holocene (the present warm period lasting
for about ten millennia).
5. Solar Activity on the Multimillennium Scale
Some features of the very long-term solar activity, such as the occurrence of grand
minima, can be studied directly from cosmogenic isotope data, e.g.,Voss (1996) and
Peristykh and Damon (2003) analyzed the filtered _14C data for the last millennia
and demonstrated the existence of the secular (known also as Gleissberg) cycle and
the 200–210-year (de Vries or Suess) cycle throughout the studied intervals. Also,
a characteristic time of about 2000–2400 years was found in the frequency of grand
minima occurrence (Vasiliev and Dergachev, 2002; Peristykh and Damon, 2003).
Although this method is applied to an analysis of grand minima and qualitative
behavior of solar activity, it cannot study the quantitative level of the activity. On the
other hand, physics-based models (Section 4.2) provide quantitative reconstructions
of solar activity which allow studying also long-term changes in the activity and,
in particular, occurrence of periods with very high activity. The modern period of
high solar activity with the average SN of about 76 after 1940 is known, from the
direct observations, to be unique since 1610. Moreover, it was shown by Usoskin
(2003b), who used a physics-based SN reconstruction from 10Be data, that never
during the last millennium was the Sun as active as it has been since 1940, while the
cycle-averaged SN did not exceed the value of 50 for the millennium before that
LONG-TERM SOLAR ACTIVITY: DIRECT AND INDIRECT STUDY 45
Figure 5. Periods of solar activity extremes according to the reconstruction by Solanki et al. (2004).
Lower panel: grand minima, corresponding to reconstructed Rg < 10. Upper panel: periods of high
activity, corresponding to reconstructed Rg > 50 and Rg > 75, as denoted in the right.
(see Figure 4). However, the multimillennia physics-based reconstruction using
14C data (Solanki et al., 2004) suggests that the present high-activity episode is
not unique but rare on the multimillennia time scale, with several similar episodes
appearing 8,000–10,000 years ago.
Figure 5 shows the periods of solar activity extremes. The lower panel depicts
grand minima which are defined as periods when the reconstructed 10-year averaged
SN did not exceed the value of 10 during at least 20 years. These periods are
close to earlier reconstructions of grand minima periods (see, e.g., Figure 2 in
Voss, 1996, who used raw _14C data). The characteristic time of 2000–2400-year
corresponding to clustering of grand minima is clear, while Gleissberg and de
Vries (Suess) periodicities in the grand minima occurrence can be traced within the
clusters. The most interesting is the upper panel of Figure 5 which shows the periods
of high solar activity, according to the reconstruction by Solanki (2004), defined
as a systematic (during at least 20 years) excess of SN over the given threshold
level. Here we show active periods for the two threshold levels, 50 and 75. Periods
when SN level exceeds 50 correspond to high solar activity. The latest (before the
present one) such episode had happened about 2400 years ago, implying again that
the modern episode is quite unique (SN level did not exceed 40 during the famous
Medieval maximum in twelfth century). The total number of such episodes is about
30 although they are not uniformly distributed – they tend to cluster around 500
BC, 1500 –3500 BC, and before 6000 BC. The threshold level of 75 corresponds
to extremely high activity episodes. There are only five such extreme episodes
(including the present one), four of which occurred before 6500 BC.
6. Concluding Remarks
We have presented a brief reviewof methods and results in studying long-term (from
centennial to multimillennium time scales) solar activity which can be summarized
as follows. Group sunspot numbers should be used instead of theWolf series for the
times before 1850. The use of a linear regression to reconstruct solar activity yields
very uncertain results. Recently developed physics-based models raise solar activity
reconstruction to the newlevel and allowstudying its behavior on the multimillennia
time scale. The frequency of the occurrence of extremes of solar activity is analyzed
using SN reconstruction by Solanki et al. (2004). The characteristic time of 2000–
2400-year as well as Gleissberg and de Vries (Suess) periodicities are apparent in
the grand minima occurrence. It is important to note that the modern episode of
very high solar activity (after 1940) is very rare in the multimillennia time scale,
through the entire Holocene. There were only four other similar episodes, all of
them occurred before 6500 BC.
We would like to see further investigations in the following directions. New
measurements of cosmogenic proxies will help disentangle the terrestrial and solar
signals. The physical models discussed here should be improved with more realistic
consideration of changing geomagnetic and climatic factors. A systematic search
for historical information on sunspot observation may resolve some uncertainties
in sunspot activity during, e.g., the eighteenth century.
We thank J¨urg Beer for useful discussions. We acknowledge financial support by
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